Scraped Surface Heat Exchangers

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Scraped Surface Heat Exchangers
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Overview of Current Research

• Problems in Fluid Dynamics and Heat Transfer
• Paradigm Problems
• Channel flow
• Thin cavity
• Blade
• Affects of wear near the tip
• Stresses acting on Blade
• 2D Flow
• Cavity
• Inter-connected chambers
• 3D Flow

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Mathematical Considerations

• Temperature dependant viscosity
• Heat thinning
• Non-Newtonian fluid
• Power-law shear thinning
• Viscous Dissipation
• Conservation
• Mass
• Momentum
• Energy

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Flow Around a Blade

• Problem Formulation
• Newtonian
• Isothermal
• Incompressible
• Lubrication approximation

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• Pressure conditions
• Far-field entry pressure must be equal to the
  pressures above and below the leading blade tip
• Far-field exit pressure must be equal to the
  pressures above and below the trailing blade tip
• For the scraper to be in equilibrium, the moment
  about the pivot due to pressure must vanish
• Blade Angle
• Independent of viscosity and the speed of the
  moving lower boundary

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• No solutions when the blade is pivoted near the
  trailing end
• Extensions
• Shear-Thinning
• Periodic blade-arrays

• Naïve contact problem has a singular force
• Asperities in blade and machine-casing surfaces
• Solid-fluid contact
• Blade wear and geometry

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Parallel Channel Flow

• Unidirectional
• Steady
• Power-law fluid
• Heat thinning
• Viscous dissipation

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Linear Stability Analysis
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Thin Cavity Problem

• Lubrication approach
• Large Peclet
• Small Brinkman
• Newtonian
• Neglect corner flow

z
y
x
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Steady 2D Problem

• FEM
• Problems
• Cavity
• Annulus with blades
• Extensions
• 3D

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Streamlines for 2D Cross Section
m1.0 m1.0 20
gap 60 gap m0.33 m0.
33 20 gap 60 gap
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Isotherms 2D Cross Section
m1 Re10 Br0.3 b0.05
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Isotherms for 3D Cavity Problem

• Re2, Br0.512, Pe3200, W/U1/8, m1.0

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Summary

• Blade flow
• Lubrication approximation and contact problems
• Blade geometry and wear
• Paradigm problems
• Stability problem for non-unique regimes in
  channel flows
• Slender cavity problems for a number of small
  parameter regimes
• Full two and three dimensional problems
• Consolidate current findings
• Numerical stability analysis